Emergence of $^4$H $J^\pi=1^-$ resonance in contact theories

TL;DR

This paper demonstrates the emergence of a stable $^4$H $J^=1^-$ resonance in contact theories using pionless EFT, revealing universal features of few-fermion systems and implications for nuclear physics.

Contribution

It shows a cutoff-stable resonance in $^4$H using three numerical methods, highlighting the importance of three-body scales and suggesting similar states in larger nuclei.

Findings

A universal $^4$H $J^=1^-$ resonance is found.

Resonance stability is independent of cutoff within a range.

Implications for powercounting in pionless EFT and larger nuclei.

Abstract

We obtain the $s$- and $p$-wave low-energy scattering parameters for n$^3$H elastic scattering and the position of the $^4$H $J^\pi=1^-$ resonance using the pionless effective field theory at leading order. Results are extracted with three numerical techniques: confining the system in a harmonic oscillator trap, solving the Faddeev-Yakubovsky equations in configuration space, and using an effective two-body cluster approach. The renormalization of the theory for the relevant amplitudes is assessed in a cutoff-regulator range between $1\,\text{fm}^{-1}$ and $10\,\text{fm}^{-1}$. Most remarkably, we find a cutoff-stable/RG-invariant resonance in the $^4$H $J^\pi=1^-$ system. This $p$-wave resonance is a universal consequence of a shallow two-body state and the introduction of a three-body $s$-wave scale set by the triton binding energy. The stabilization of a resonant state in a few-fermion system through pure contact interactions has a significant consequence for the powercounting of the pionless theory. Specifically, it suggests the appearance of similar resonant states also in larger nuclei, like 16-oxygen, in which the theory's leading order does not predict stable states. Those resonances would provide a starting state to be moved to the correct physical position by the perturbative insertion of sub-leading orders, possibly resolving the discrepancy between data and contact EFT.